Fractional Integrals Potentials and Radon Transforms 2nd Edition By Boris Rubin

The book Fractional Integrals, Potentials, and Radon Transforms 2nd Edition by Boris Rubin talks about special math ideas used in science and engineering.

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Preliminaries
- Integral inequalities and maximal functions
- Integral operators with homogeneous kernels
- Gamma and beta functions
- Spherical harmonics
- Fourier transform and distributions (etc.)
Basics of One‑Dimensional Fractional Integration
- Definitions, properties, fractional derivatives, potentials (etc.)
Comparison of Ranges and Mapping Properties
- Singular integrals, weighted spaces, restrictions, extensions (etc.)
Local Properties and the Critical Exponent
- Local estimates, relationships between integrals, BMO approach (etc.)
Marchaud’s Method
- Finite differences, analytic continuation, generalized methods (etc.)
Fractional Integrals and Wavelet Transforms
- Calderón reproducing formula, wavelet type integrals and representations (etc.)
Potentials on Rⁿ
- Riesz, Helmholtz, and Bessel potentials (etc.)
One‑Sided Riesz Potentials
- Definitions, inversion formulas, restrictions, factorization (etc.)
One‑Sided Helmholtz Potentials
- Kernels of Poisson type, inversion, extensions (etc.)
Ball Fractional Integrals

Definitions, mapping properties, harmonic analysis (etc.)

Fractional Integrals on the Unit Sphere

Approximate identities, spherical potentials, wavelet transforms (etc.)

Fractional Integrals in Integral Geometry

k‑plane transforms, Funk transforms, hyperbolic space geometry (etc.)

Gårding‑Gindikin Integrals and Radon Transforms

Matrix analysis prerequisites, Radon transforms, inversion (etc.)
Appendix: Operators commuting with rotations and dilations.

MAECENAS IACULIS

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ADIPISCING CONVALLIS BULUM

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